(d) Calculate the value of dx correct to 3 significant figures taking six intervals by Trapezoidal Rule.

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Q: Sketch a graph of y = 8 on [- 5, 4] and use geometry to find the exact value of int -5 ^ 4 8 dx.

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Q: correct to three decimal places by Trapezoidal rule with 1 +x dx Evaluate I= h=0-5.

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Q: 2. Use the composite trapezoidal rule with the step length h = 0.1 to evaluate dx I = 1+x2 and…

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Q: Estimate sinx? dx with an error of less than 0.001.

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Q: Use the Midpoint Rule with = 4 to approximate 0 tan x dx.

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Q: Calculate the deriv L tan2tdt d_ dx II

A: Derivation of          is calculated as shown below

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Q: Use the Midpoint Rule with n = 4 to estimate (x² + 1) dx %3D

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Q: dx 4.Exaluate I=| correct to three decimal places by Trapezoidal rule with h=0-25.

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Q: 3 dx by Simpson's rule breaking it into 6 intervals. Evaluate 2+x?

A: We have to evaluate the integral ∫2532+x2dx by Simpson's rule-breaking it into 6 intervals.

Q: How do you use a Maclaurin serieis aproximation to estimate (Provided picture). Thanks!

A: First find the Maclaurin series for e^(x^2) using the Maclaurin series of e^xPlug x^2 in place of x.

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Q: 4 1 -dx using the midpoint rule with three subdivisions to four decimal places. In(x) Approximate…

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Q: The accompanying table shows the velocity of a model train engine moving along a track for 10…

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A: Given that 25 tents are built and the average number of COVID cases per tent will be 6 caseswhile…

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A: We need to find rate at which COVID cases is increasing.

Q: Use the midpoint rule to calculate the absolute error of (4x² + 1) dx using 3 subintervals. Enter an…

A: Given query is to find the absolute error of Integral.

Q: x = -sin 2y x = cos y --

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Q: 1. Use the trapezoidal rule with eight intervals to evaluate places. I = [dx 3 2 %3D correct to 3…

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Q: Use Simpson's rule with 3 8 intervals, to evaluate 2 dx, correct to 3 decimal places.

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Q: Use the trapezoidal rule with n = 2 to approximate the value of sin(x²)dx. Round your answer to four…

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Q: 1 dx -1 2x+3 a.

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Q: What is the area of the region between the sine curve and the x-axis from to 2 ? -1 2 1 4 3.

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Q: I Approximate "dn with accuracy l by te modified Trapozoidal Compo site rule.

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Q: rea of the region between the sine curve

A: Here we have to find the area of the region bounded by the sine curve and the x-axis from π2 to 2π.…

Q: Use the trapezium rule to find [2" dx taking ordinates with interval 0.25, in three decimal places.

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Q: By using Trapezoidal rule, the value of “h" in evaluating (x² – 2x + 6)dx , by taking 10…

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Q: dx -1 2x+3

A: To solve the following integral

Q: 4x dx.

A: Given I=∫02e-4xdx Here fx=e-4x,a=0,b=2,n=4 . Then h=b-an=12 Therefore, the subintervals are…

Q: Use Simpson's rule to evaluate 1 -dx, by dividing the interval into 4 equal (5x-2) parts. Find the…

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Q: 1 Evaluate dx by using Trapezoidal rule. Hence obtain 1 + x2 he approximate value of .

A: I am attaching image so that you understand each and every step.

Q: Approximate sinx dx using four trapezoids of equal width. On the interval (0, pi)

A: Trapezoidal rule

Q: Estimate 4 - x dx using midpoints for n= 4 approximating rectangles. 2 4 – x dx is approximately

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A: To Find: The rate at which the total average number of COVID cases dx is increasing at x = 10 tents…

Q: The approximate value of dx by using Simpson's rule is 0.3480, then the error in the approximation…

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Q: Use Trapezoidal rule with 5 subintervals and 8 subintervals to find an approximation of x3V-2x4 +…

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Q: To approximate cos(x) dx would Simpson's Rule, Midpoint Rule, or Trapezoidal Rule give a better…

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Q: Using Trapezoidal Rule, with 6 intervals, Evaluate 2 2x dx , correct to 3 2+x2 decimal places

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Q: Using Simpson's rule, what is the approximate value of ſ dx with n 10?

A: Given that, the integral is ∫0211+x3dx and the value of n=10. Note that, the Simpson's rule…

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Q: 5) Approximate -dx 1 +: Using the Trapezoidal rule and Simpson's rule with h=1. Find an error in…

A: We have to use both numerical methods for 4 subintervals as h=1 and (b-a)=4.

Q: Use Trapezoidal method to evaluate (2x/2-x dx, by dividing the interval into 4 1 equal parts. Find…

A: According to question given that∫122x2-x2dxn=4

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.